Heat Transport in Cuprates

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Heat Transport in Cuprates
Louis Taillefer University of Toronto
Université de Sherbrooke Canadian Institute for
Advanced Research
Quantum Materials Program meeting, Vancouver, 16
May 2003
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University of Toronto
Rob Hill Cyril Proust Filip Ronning Makariy
Tanatar Harry Zhang
Etienne Boaknin Dave Hawthorn Johnpierre Paglione
Mike Sutherland
Doug Bonn University of British Columbia Walter
Hardy Ruixing Liang Shuichi Wakimoto University
of Toronto Robert Birgeneau Patrick
Fournier Université de Sherbrooke Jeff
Sonier Simon Fraser University
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Collaborators
R.L. Greene University of Maryland A.P.
Mackenzie University of St-Andrews N.E.
Hussey University of Bristol R. Gagnon
McGill University T. Kimura University of
Tokyo M. Nohara H. Takagi
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Thermal conductivity primer
k kelectrons kphonons
k0 / T ?
Residual linear term
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Phonons beyond Casimir T3 limit
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Phonons beyond Casimir T3 limit
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Part I H 0
Superconducting state
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Fermi-liquid theory of nodal quasiparticles

• Thermal metal

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d-wave superconductivity Nodal quasiparticles in
cuprates
thermal conductivity
jQ // a axis
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Doping dependence
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Doping dependence
doping independent !!
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Fermi Surface Node
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Fermi Surface Node
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Nodal quasiparticles in underdoped Cuprates
YBCO
?
DBCS 4kBTc
Sutherland et al. PRB (2003) cond-mat / 0301105
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Part I H 0
Superconducting state
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Part I H 0
Superconducting state

• Nodal d-wave quasiparticles EVERYWHERE in
  superconducting dome
• ? no complex component ANYWHERE (no dix)

Paper Sutherland et al., cond-mat/0301105
POSTER
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Digression 1 Residual linear term in clean
underdoped cuprates
? clear linear term
Also present in highly-ordered stoichiometric
YBCO 6.50 (ortho-II)
Sutherland et al., cond-mat/0301105 POSTER
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Part I H 0
Superconducting state

• Nodal d-wave quasiparticles EVERYWHERE in
  superconducting dome
• ? no complex component ANYWHERE (no dix)

Paper Sutherland et al., cond-mat/0301105
POSTER
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Part I H 0
Superconducting state

• Nodal d-wave quasiparticles EVERYWHERE in
  superconducting dome
• ? no complex component ANYWHERE (no dix)
• Low-energy gap tracks high-energy pseudogap
• ? pseudogap most likely SUPERCONDUCTING

Paper Sutherland et al., cond-mat/0301105
POSTER
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Digression 2 Effect of disorder in using heat
transport to measure the gap
? ? 1 10 100
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Digression 2 Effect of disorder in using heat
transport to measure the gap
? Universal limit formula only valid in CLEAN
LIMIT
YBCO ? Clean limit

• LSCO
• NOT clean limit
• (cannot use d-wave formula)

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Digression 3 Temperature dependence of
electronic heat transport
Ultrapure YBCO near optimal doping
Hill et al., preprint POSTER
Carbotte, Marsiglio Theory
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Part II H gt 0
A. Superconducting state
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D-wave Superconductor in Magnetic Field
Semi-classical description
QP D.O.S increases
Volovik effect
Corresponding increase in thermal conductivity
G.E.Volovik, JETP Lett. 58 469 (1993)
May Chiao et al., PRL 82, 2943 (1999).
Quasiparticles have energy Doppler shifted
through coupling to the superfluid flow around
each vortex.
C. Kübert and P.J. Hirschfeld, PRL 80, 4963
(1998).
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D-wave Superconductor in Magnetic Field
Semi-classical description
QP D.O.S increases
Volovik effect
Corresponding increase in thermal conductivity
G.E.Volovik, JETP Lett. 58 469 (1993)
May Chiao et al., PRL 82, 2943 (1999).
Quasiparticles have energy Doppler shifted
through coupling to the superfluid flow around
each vortex.
C. Kübert and P.J. Hirschfeld, PRL 80, 4963
(1998).
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Digression 3 Anomalous behavior in vortex state
of s-wave superconductors
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Digression 3 Anomalous behavior in vortex state
of s-wave superconductors
Boaknin et al., PRL 90, 117003 (2003)
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Digression 3 Anomalous behavior in vortex state
of s-wave superconductors
ANOMALOUS
NbSe2 s-wave superconductor
? Two regimes
Two-band superconductivity
Boaknin et al., PRL 90, 117003 (2003)
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Vortex state of d-wave superconductors at T ? 0
LSCO as a function of doping
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Part II H gt 0
A. Superconducting state

• Vortex state of d-wave superconductors at T ? 0
  
• ? YBCO increase in conduction with field
• Paper Hill et al., preprint POSTER

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Part II H gt 0
A. Superconducting state

• Vortex state of d-wave superconductors at T ? 0
  
• ? YBCO increase in conduction with field
• Paper Hill et al., preprint POSTER
• ? Underdoped LSCO decrease in conduction with
  field
• Paper Hawthorn et al., PRL 90, 197004
  (2003) POSTER

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Part II H gt 0
B. Normal state
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Overdoped
Tl2Ba2CuO6d
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Overdoped
Tl2Ba2CuO6d
heat transport
H 0
13 T
? Wiedemann-Franz law is perfectly obeyed
Proust et al., PRL 89, 147003 (2002)
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Digression 5 No evidence of swiss cheese
effects in overdoped Tl-2201
?N / T ?
?S / T ?
?S / ?N 1/3 ? f lt 1/3 ?BCS / ?S
78 ? f lt 10
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(No Transcript)
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Pr1.85Ce0.15CuO4
Exceeds WFL by factor 2
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field-induced normal state ? insulator
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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La1.94Sr0.06CuO4
Underdoped
heat transport
? field-induced thermal METAL ? INSULATOR
transition
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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La1.94Sr0.06CuO4
Underdoped
heat transport
thermal M-I transition
Hawthorn et al., PRL 90, 197004 (2003) POSTER
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Part II H gt 0
B. Normal state

• Overdoped regime
• ? Fermi-liquid ground state (Tl-2201)
• Paper Proust et al., Phys. Rev. Lett. 89,
  147003 (2002)

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Part II H gt 0
B. Normal state

• Overdoped regime
• ? Fermi-liquid ground state (Tl-2201)
• Paper Proust et al., Phys. Rev. Lett. 89,
  147003 (2002)
• Optimally-doped regime
• ? Violation of Wiedemann-Franz law (PCCO)
• Paper Hill et al., Nature 414, 711 (2001)

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Part II H gt 0
B. Normal state

• Overdoped regime
• ? Fermi-liquid ground state (Tl-2201)
• Paper Proust et al., Phys. Rev. Lett. 89,
  147003 (2002)
• Optimally-doped regime
• ? Violation of Wiedemann-Franz law (PCCO)
• Paper Hill et al., Nature 414, 711 (2001)
• Underdoped regime
• ? Thermal Metal-Insulator transition (LSCO)
• Paper Hawthorn et al., PRL 90, 197004
  (2003) POSTER

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Digression 6 Nature of low-energy excitations
at a QCP ?

• Magnetic-field-induced T 0 phase transitions
• Metamagnetic Sr3Ru2O7 Poster
  Ronning et al.
• Superconducting ? CeCoIn5
• Paper Paglione et al.,
  cond-mat/0211312

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The End